First, it should be noted that Christianity began against the background of a fraught relationship between Jews and the Roman Empire. Jewish rebellions were an ongoing problem for Rome. Part of declaring loyalty to the Roman Empire was offering incense to the cult of the Roman Emperor. Jews and Christians refused to do this on the basis that it constituted idolatry. In the view of the Romans, the problem was not the religion of their conquered territories, but that they were committing treason.
Many of these quotations were intended to show that Christians were indeed loyal and obedient Roman citizens. The famous quotation "Render unto Caesar the things that are Caesar's ... " and also "My kingdom is not of this world" (John 18:36) both suggest a sort of quietism. They suggest that Christians should focus on God's world and let secular rulers deal with secular matters. Much of the notion of "separation of church and state" in the United States Constitution reflects this attitude. The three other quotations suggest an attitude of greater subordination to authority; one which led eventually to Christianity becoming a state religion. The main context is one where the second coming of Christ was expected soon; thus, the emphasis was avoiding conflict with secular societies and focusing on the next world.
Confucian beliefs were not grounded in the notion of an afterlife. They were concerned with the duty of the individual to family and society. Rather than recommending disengagement from society and politics, Confucius recommends engagement and sees virtue as embedded within and grounded by social and political context. The ideal Christian submits to authority because, ultimately, worldly authority is unimportant, while the follower of Confucius lives in harmony with state authority (submitting, although trying to reform by example) because virtue is civic in nature.